Quantum function algebras from finite-dimensional Nichols algebras,

FARINATI, MARCO Y GARCÍA, GASTÓN

JOURNAL OF NONCOMMUTATIVE GEOMETRY

EUROPEAN MATHEMATICAL SOC

Lugar: Zürich; Año: 2020

1661-6952

We describe how to find quantum determinants and antipode formulas frombraided vector spaces using the FRT-construction and finite-dimensional Nicholsalgebras. It generalizes the construction of quantum function algebras usingquantum grassmanian algebras. Given a finite-dimensional Nichols algebra B, ourmethod provides a Hopf algebra H such that B is a braided Hopf algebra in thecategory of H-comodules. It also serves as source to produce Hopf algebrasgenerated by cosemisimple subcoalgebras, which are of interest for thegeneralized lifting method. We give several examples, among them quantumfunction algebras from Fomin-Kirillov algebras associated with the symmetricgroups on three letters.